In this video, we study the power of wind and how much power can be extracted as useful electrical energy. We seek to know how much energy or power is available from the wind. To answer this larger question, we answer these three smaller questions. How does the wind speed relate to wind energy and power? How does wind speed translate to energy from the wind? How does power from the wind affect wind turbine design? Let's first calculate the energy in wind, or more precisely, the power of wind. Recall from high school physics that we can calculate the kinetic energy of a moving object as, kinetic energy equals 1/2 mass times velocity squared. But what is the mass of wind? Wind is an object, it's a moving fluid, so it's hard to put it on a scale to determine its weight mass. But we can measure or estimate its mass, is the volume of air with density rho that passes through a fixed circle of area a per second. So that mass is equal to rho times area times the velocity per second. Note that since we are measuring mass per second, we're not measuring energy, but rather power, which we know is energy per second. Therefore, the power of air can be measured by substituting mass per second into our kinetic energy equation. Collecting terms, we get the power of wind as 1/2 density times area times velocity of wind cubed to the third power. This is a very important result. The graph to the right illustrates how the power of wind increases with the cube of its velocity. This means that wind blowing at 10 meters per second has eight times the power of wind blowing at five meters per second. The graph to the right illustrates this. Observe that the power of wind blowing at about 25 meters per second, is almost 10 kilowatts, while wind blowing at 50 meters per second is almost 80 kilowatts, eight times more powerful. For our purposes, it is not so important to remember the derivation of this result but the power formula itself. But what is important is the qualitative insight that the power of wind increases as the cube of its velocity. Really important. Why is this result regarding the power of wind so important? To answer this question, recall this graph from a previous video. The graph shows how a wind speeds vary over time, say a year, by representing wind speeds as a frequency distribution. Specifically, this graph shows the number of hours that wind blows at a certain speed during the 8,760 hours of year. For example, for this distribution, we see that wind blows at eight miles per second or make that meters per second for about 800 hours each year. Now, what's this mean as far as power? How does wind speed variability translate into wind power? The red curve here shows the distribution of wind speeds over the 8,760 hours of a year, similar to the graph we just looked at. The blue curve shows the energy output in megawatt hours from a typical wind turbine over the same year. Several important observations. Note that the wind, or the average wind speed during the year is about seven meters per second. The amount of energy from winds at seven meters per second or less is only about 10 percent of the total energy from the wind turbine. This means that 90 percent of energy out of the turbine occurs at wind speeds above average. Further observed that the 25 percent of energy output occurs when wind speeds are greater than 15 meters per second. But that these wind speeds occur rarely during the year, perhaps only five percent of the time. The critical insight here is that mean wind speeds are less important than the frequency distribution of higher speeds that are greater than the mean. When choosing a site for a wind farm, high-speed winds are critically important. This result plus insights from the previous video on wind characteristics, allow us to answer the question, how does power from the wind affect wind turbine design? First, we have seen that high wind speeds are desired. Power comes from high wind speeds, since power increases with the cube of velocity v. A large blade radius produces more power since it's swept area increases with the square of the radius r, and power increases linearly with area. So power increases as the square of radius. Tall towers are preferred to short towers since wind velocity, v increases with height. Smooth terrain is preferred to rough landscape since smooth terrain provides greater velocity at a lower height. Smooth seas are best while rough urban or mountainous areas are worse for generating wind power. Finally, dense air provides more energy, so sea level provides greater air density than high altitudes. We're now able to answer the questions we posed at the start of this video. Answering the question, how does wind speed relate to wind energy and power? We now know that wind power increases as the cube of wind velocity. Answering how does wind speed translate to wind energy and power? We can now say that high-speed winds provide the bulk of wind energy and wind power. Answering, how does power from the wind affect wind turbine design? We understand that factors affecting wind turbine design are tower height, radius of blades and the wind speeds, roughness, and altitude of a specific location. In the next video, we'll take a closer look at wind site evaluation, which combines all of these factors. Will see you there.
